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FieldLUDecomposition (Commons Math 3.2 API)
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org.apache.commons.math3.linear</FONT>
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Class FieldLUDecomposition&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt;</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.linear.FieldLUDecomposition&lt;T&gt;</B>
</PRE>
<DL>
<DT><DT><B>Type Parameters:</B><DD><CODE>T</CODE> - the type of the field elements</DL>
<HR>
<DL>
<DT><PRE>public class <B>FieldLUDecomposition&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt;</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></DL>
</PRE>

<P>
Calculates the LUP-decomposition of a square matrix.
 <p>The LUP-decomposition of a matrix A consists of three matrices
 L, U and P that satisfy: PA = LU, L is lower triangular, and U is
 upper triangular and P is a permutation matrix. All matrices are
 m&times;m.</p>
 <p>Since <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3"><CODE>field elements</CODE></A> do not provide an ordering
 operator, the permutation matrix is computed here only in order to avoid
 a zero pivot element, no attempt is done to get the largest pivot
 element.</p>
 <p>This class is based on the class with similar name from the
 <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library.</p>
 <ul>
   <li>a <A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getP()"><CODE>getP</CODE></A> method has been added,</li>
   <li>the <code>det</code> method has been renamed as <A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getDeterminant()"><CODE>getDeterminant</CODE></A>,</li>
   <li>the <code>getDoublePivot</code> method has been removed (but the int based
   <A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getPivot()"><CODE>getPivot</CODE></A> method has been kept),</li>
   <li>the <code>solve</code> and <code>isNonSingular</code> methods have been replaced
   by a <A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getSolver()"><CODE>getSolver</CODE></A> method and the equivalent methods
   provided by the returned <A HREF="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear"><CODE>DecompositionSolver</CODE></A>.</li>
 </ul>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>2.0 (changed to concrete class in 3.0)</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: FieldLUDecomposition.java 1449528 2013-02-24 19:06:20Z luc $</DD>
<DT><B>See Also:</B><DD><a href="http://mathworld.wolfram.com/LUDecomposition.html">MathWorld</a>, 
<a href="http://en.wikipedia.org/wiki/LU_decomposition">Wikipedia</a></DL>
<HR>

<P>

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<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#FieldLUDecomposition(org.apache.commons.math3.linear.FieldMatrix)">FieldLUDecomposition</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A>&gt;&nbsp;matrix)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Calculates the LU-decomposition of the given matrix.</TD>
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<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getDeterminant()">getDeterminant</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Return the determinant of the matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getL()">getL</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the matrix L of the decomposition.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getP()">getP</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the P rows permutation matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;int[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getPivot()">getPivot</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the pivot permutation vector.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="interface in org.apache.commons.math3.linear">FieldDecompositionSolver</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getSolver()">getSolver</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get a solver for finding the A &times; X = B solution in exact linear sense.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getU()">getU</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the matrix U of the decomposition.</TD>
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<A NAME="FieldLUDecomposition(org.apache.commons.math3.linear.FieldMatrix)"><!-- --></A><H3>
FieldLUDecomposition</H3>
<PRE>
public <B>FieldLUDecomposition</B>(<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A>&gt;&nbsp;matrix)</PRE>
<DL>
<DD>Calculates the LU-decomposition of the given matrix.
<P>
<DL>
<DT><B>Parameters:</B><DD><CODE>matrix</CODE> - The matrix to decompose.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</A></CODE> - if matrix is not square</DL>
</DL>

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<A NAME="getL()"><!-- --></A><H3>
getL</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A>&gt; <B>getL</B>()</PRE>
<DL>
<DD>Returns the matrix L of the decomposition.
 <p>L is a lower-triangular matrix</p>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the L matrix (or null if decomposed matrix is singular)</DL>
</DD>
</DL>
<HR>

<A NAME="getU()"><!-- --></A><H3>
getU</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A>&gt; <B>getU</B>()</PRE>
<DL>
<DD>Returns the matrix U of the decomposition.
 <p>U is an upper-triangular matrix</p>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the U matrix (or null if decomposed matrix is singular)</DL>
</DD>
</DL>
<HR>

<A NAME="getP()"><!-- --></A><H3>
getP</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A>&gt; <B>getP</B>()</PRE>
<DL>
<DD>Returns the P rows permutation matrix.
 <p>P is a sparse matrix with exactly one element set to 1.0 in
 each row and each column, all other elements being set to 0.0.</p>
 <p>The positions of the 1 elements are given by the <A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getPivot()"><CODE>pivot permutation vector</CODE></A>.</p>
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the P rows permutation matrix (or null if decomposed matrix is singular)<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getPivot()"><CODE>getPivot()</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="getPivot()"><!-- --></A><H3>
getPivot</H3>
<PRE>
public int[] <B>getPivot</B>()</PRE>
<DL>
<DD>Returns the pivot permutation vector.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>the pivot permutation vector<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html#getP()"><CODE>getP()</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="getDeterminant()"><!-- --></A><H3>
getDeterminant</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A> <B>getDeterminant</B>()</PRE>
<DL>
<DD>Return the determinant of the matrix.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>determinant of the matrix</DL>
</DD>
</DL>
<HR>

<A NAME="getSolver()"><!-- --></A><H3>
getSolver</H3>
<PRE>
public <A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="interface in org.apache.commons.math3.linear">FieldDecompositionSolver</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="type parameter in FieldLUDecomposition">T</A>&gt; <B>getSolver</B>()</PRE>
<DL>
<DD>Get a solver for finding the A &times; X = B solution in exact linear sense.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>a solver</DL>
</DD>
</DL>
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